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We study in this paper a respond of an elastic half-plane to random boundary excitations. We treat both the white noise excitations
and more generally, homogeneous random fluctuations of displacements prescribed on the boundary. Solutions to these problems
are inhomogeneous random fields which are however homogeneous with respect to the longitudinal coordinate. This is used to
represent the displacements as series expansions involving a complete set of deterministic functions with corresponding random
coefficients. We construct the Karhunen-Loève (K-L) series expansion which is based on the eigen-decomposition of the correlation
operator. The K-L expansion can be used to calculate the statistical characteristics of other functionals of interest, in
particular, the strain and stress tensors and the elastic energy tensor.
This work is supported partly by the RFBR Grant N 06-01-00498.
I. Shalimova acknowledges the host institute WIAS, Berlin, and the support of DFG, under Grant SA 861/6-1 of 2008. 相似文献